Vladimir Putin and Donald Trump discuss mending ties

Obama sought to reassure in his first news conference since Trump's stunning win [EPA]

Russian President Vladimir Putin and US president-elect Donald Trump have spoken over the phone to discuss efforts to improve US-Russian ties, the Kremlin and Trump's office said.

"President-elect Trump noted to President Putin that he is very much looking forward to having a strong and enduring relationship with Russia and the people of Russia," Trump's office said in a statement on Monday.

The Kremlin, in a far more specific and longer statement, said that Putin congratulated Trump on his victory and expressed Russia's readiness to "establish a partner-like dialogue with the new administration on the basis of equality, mutual respect and non-interference in domestic relations".

"During the call, the two leaders discussed a range of issues including the threats and challenges facing the United States and Russia, strategic economic issues and the historical US-Russia relationship that dates back over 200 years," Trump's office said.

In its statement, the Kremlin said Putin and Trump agreed that US-Russian ties were in "extremely unsatisfactory" condition.

Syria's civil war

The two also agreed on the need to combine efforts in the fight against "international terrorism and extremism" and discussed settling the Syrian war in that context, according to the Kremlin.

How to fight side-by-side in Syria, where Russia supports President Bashar al-Assad and the US supports rebels fighting against him, and also against the Islamic State of Iraq and the Levant group (ISIL, also known as ISIS), has been one of the key sticking points between US President Barack Obama and Putin.

The Kremlin said that Putin and Trump agreed to continue phone contact and to plan a personal meeting in the future.

Obama began his presidency with a goal to "reset" ties with Russia, but they eventually plunged to the lowest point since the Cold War over the conflicts in Ukraine and Syria.

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Separately, vouching for the successor he never imagined having, Obama on Monday sought to reassure an anxious nation and world that Trump would maintain US alliances and influence.

"There is enormous continuity ... that makes us that indispensable nation when it comes to maintaining order around the world," Obama said.

Relationships and policies go beyond presidents, he said, adding that military officials, diplomats and intelligence officers would cooperate with their foreign counterparts as before.

In a White House meeting with Trump last week, Obama said the Republican "expressed a great interest in maintaining our core strategic relationships", including "strong and robust NATO" partnerships.

It was a sharp change in tone for Obama, who regularly mocked Trump's candidacy in the last days before the election, even accusing the billionaire businessman and former reality television star of helping ISIL with his rhetoric about Muslims and undermining US democracy through his claims of a "rigged" election.

At the time, almost all polls showed Democrat Hillary Clinton leading Trump.